Oscillations of a Circular Cylinder in a Linearly Stratified Fluid

The plane problem of the motions of a three-layer fluid initiated by the oscillations of a circular cylinder is solved in the linear formulation in the Boussinesq approximation. The cylinder is completely immersed in the linearly stratified middle layer, and the upper and lower layers are homogeneous and bounded by rigid horizontal walls. The fluid is assumed to be ideal and incompressible. The added mass and damping coefficients are calculated as functions of the oscillation frequency of the cylinder and the layer thicknesses.     

Heat transfer in a horizontal fluid layer heated from below upon rotation of one of the boundaries

The mixed convection in a horizontal fluid layer which is generated by uniform heating from below and by rotation of one of the boundaries of the layer was studied experimentally. The region occupied by the fluid is a cylinder of radius320 mm and height45 mm. Either the upper or the lower boundary together with the side wall rotates. For Rayleigh numbersRa≃2·10 ⁷, in a broad range of Reynolds numbers, based on experimental data we constructed mean-temperature profiles along the normal to the upper boundary and with a uniform step over the radius. In addition, we obtained data on the radial thermal stratification of the fluid, the integral flow through the fluid layer, and information on temperature fluctuations. The complicated character of the dependence of the heat transfer on the Reynolds number was shown. The obtained dependences of the heat transfer and temperature inhomogeneity on Reynolds numbers was explained qualitatively. Kutateladze Institute of Thermal Physics, Siberian Division, Russian Academy of Sciences, Novosibirsk 630090. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 39, No. 3, pp. 126–133, May–June, 1998.     

Plane waves in a heavy two-layer liquid excited by a cylinder moving at an angle to the horizontal

A solution of an initial-boundary-value problem for a system of integrodifferential equations which describes the plane waves excited in an initially stationary heavy two-layer ideal fluid by a cylinder moving at an angle to the horizontal is investigated. The homogeneous fluid fractions of different densities are assumed to be separated by an evolving fluid interface (horizontal plane, if the liquid is at rest). An approximate solution of two problems for the waves excited by a cylinder moving with a constant acceleration and an oscillating cylinder is constructed analytically. Nizhnii Novgorod. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 4, pp. 137–152, July–August, 1998.     

Oscillations of a cylinder piercing a linearly stratified fluid layer

The plane problem of the small steady-state oscillations of a horizontal cylinder arbitrarily located in a three-layer fluid whose upper and lower layers are homogeneous and whose middle layer is linearly stratified is considered in the linear formulation using the Boussinesq approximation. The fluid is assumed to be ideal and incompressible. The method of mass sources distributed along the body contour is used in the internal wave generation regime and an integral equation for the fluid pressure is derived in the non-wave regime. The hydrodynamic load acting on the body is calculated as a function of the oscillation frequency of the cylinder and its location. The results are compared with experimental data.     

The onset of buoyancy-driven convection in a ferromagnetic fluid saturated porous medium

The onset of buoyancy-driven convection in an initially quiescent ferrofluid saturated horizontal porous layer in the presence of a uniform vertical magnetic field is investigated. The Brinkman-Lapwood extended Darcy equation with fluid viscosity different from effective viscosity is used to describe the flow in the porous medium. The lower boundary of the porous layer is assumed to be rigid-paramagnetic, while the upper paramagnetic boundary is considered to be either rigid or stress-free. The thermal conditions include fixed heat flux at the lower boundary, and a general convective–radiative exchange at the upper boundary, which encompasses fixed temperature and fixed heat flux as particular cases. The resulting eigenvalue problem is solved numerically using the Galerkin technique. It is found that increase in the Biot number Bi, porous parameter σ, viscosity ratio Λ, magnetic susceptibility χ, and decrease in the magnetic number M ₁ and non-linearity of magnetization M ₃ is to delay the onset of ferroconvection in a porous medium. Further, increase in M ₁, M ₃, and decrease in χ, Λ, σ and Bi is to decrease the size of convection cells.     

Effect of Internal Heat Generation on the Onset of Marangoni Convection in a Fluid Layer Overlying a Layer of an Anisotropic Porous Medium

Linear stability analysis has been performed to investigate the effect of internal heat generation on the criterion for the onset of Marangoni convection in a two-layer system comprising an incompressible fluid-saturated anisotropic porous layer over which lies a layer of the same fluid. The upper non-deformable free surface and the lower rigid surface are assumed to be insulated to temperature perturbations. The fluid flow in the porous layer is governed by the modified Darcy equation and the Beavers–Joseph empirical slip condition is employed at the interface between the two layers. The resulting eigenvalue problem is solved exactly. Besides, analytical expression for the critical Marangoni number is also obtained by using regular perturbation technique with wave number as a perturbation parameter. The effect of internal heating in the porous layer alone exhibits more stabilizing effect on the system compared to its presence in both fluid and porous layers and the system is least stable if the internal heating is in fluid layer alone. It is found that an increase in the value of mechanical anisotropy parameter is to hasten the onset of Marangoni convection while an opposite trend is noticed with increasing thermal anisotropy parameter. Besides, the possibilities of controlling (suppress or augment) Marangoni convection is discussed in detail.     

Azimuthal wave motions on the surface of a rotating fluid cylinder

Wave motions in a fluid cylinder rotating about the axis are investigated within the framework of the linear theory. The cylinder is assumed to be fairly long. This makes it possible to restrict attention to the study of the plane oscillation pattern. The fluid is assumed to be ideal and incompressible. The models in which the fluid particles are confined by gravitational (body) or/and capillary forces (surface stress forces) are considered. A mode analysis is carried out and the dispersion relations are constructed. Traveling and steady-state waves on the surface of the fluid cylinder are investigated; qualitative effects ("wave inertia") are established. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 3, pp. 128–133, May–June, 1998. The work was carried out with financial support from the Russian Foundation for Basic Research (project No. 96-01-00221). An erratum to this article is available at .     

Structure of stratified flow around a cylinder at low internal froude number

The flow pattern around a horizontal cylinder towed at constant velocity in a continuously stratified fluid is visualized by the shadow method. The velocities in the leading flow disturbance, i. e., in the flow-blocking region ahead of the cylinder, are presented. In the body wake, a new class of small-size structures in the density gradient field is revealed against the background of a smooth velocity profile. The evolution of the flow pattern with variation of the parameters of body motion is studied. Institute of Mechanics Problems, Moscow 117526. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 40, No. 1, pp. 80–88, January–February, 1999.     

The effect of particles on fluid turbulence in a turbulent boundary layer over a cylinder

The turbulent fluid and particle interaction in the turbulent boundary layer for cross flow over a cylinder has been experimentally studied. A phase-Doppler anemometer was used to measure the mean and fluctuating velocities of both phases. Two size ranges of particles (30μm–60μm and 80μm–150μm) at certain concentrations were used for considering the effects of particle sizes on the mean velocity profiles and on the turbulent intensity levels. The measurements clearly demonstrated that the larger particles damped fluid turbulence. For the smaller particles, this damping effect was less noticeable. The measurements further showed a delay in the separation point for two phase turbulent cross flow over a cylinder. The project supported by the National Natural Science Foundation of China     

PIV measurements of flow past a confined cylinder

This study investigates the flow past a confined circular cylinder built into a narrow rectangular duct with a Reynolds number range of 1,500 ≤ Re _d ≤ 6,150, by employing the particle image velocimetry technique. In order to better explain the 3-D flow behaviour in the juncture regions of the lower and upper plates and the cylinder, respectively, as well as the dynamics of the horseshoe vortex system, both time-averaged and instantaneous flow data are presented for regions upstream and downstream of the cylinder. The size, intensity and interaction of the vortex systems vary substantially with the Reynolds number. Although the narrow rectangular duct with a single built-in cylinder is a geometrically symmetrical arrrangement, instantaneous flow data have revealed that the flow structures in both the lower and upper plate–cylinder junction regions are not symmetrical with respect to the centreline of the flow passage. The vortical flow structures obtained in side-view planes become dominant sometimes in the lower juncture region and sometimes in the upper juncture region in unsteady mode.     

Mixed convection boundary layer flow of a viscoelastic fluid over a horizontal circular cylinder

The steady mixed convection boundary layer flow of a viscoelastic fluid over a horizontal circular cylinder in a stream flowing vertically upwards is numerically studied for both cases of heated and cooled cylinders. The governing partial differential equations are transformed into dimensionless forms using an appropriate transformation and then solved numerically using the Keller-box method. The comparison between the solutions obtained and those for a Newtonian fluid is found to be very good. Effects of the mixed convection and elasticity parameters on the skin friction and heat transfer coefficients for a fluid having the Prandtl number equal to one are also discussed. It is found that for some values of the viscoelastic parameter and some negative values of the mixed convection parameter (opposing flow) the boundary layer separates from the cylinder. Heating the cylinder delays separation and can, if the cylinder is warm enough, suppress the separation completely. Similar to the case of a Newtonian fluid, cooling the cylinder brings the separation point nearer to the lower stagnation point. However, for a sufficiently cold cylinder there will not be a boundary layer.     

Nonlinear regimes of convection of an elasticoviscous fluid in a closed cavity heated from below

The two-dimensional thermal convection of a elasticoviscous fluid in a horizontal cylinder with a square cross-section heated from below is investigated. For describing the rheological properties of the fluid the Oldroyd model with the upper convective derivative is used. The investigation is carried out numerically using the finite-difference method. The instability limits of mechanical equilibrium with respect to monotonic and oscillatory perturbations are determined. Supercritical convection regimes are investigated numerically. Perm. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 4, pp. 5–11, July–August, 2000. This work was carried out with financial support from the Program of State Financial Support for Leading Science Schools (grant No. 96-15-96084).     

Viscous flow in a partially-filled horizontal cylinder rotating at constant speed

The problem under consideration is that of the stationary shape of the free surface of a viscous fluid in a steadily rotating horizontal cylinder. In the majority of investigations of this problem the thickness of the fluid layer coating the inner surface of the cylinder is assumed to be small [1–3]. The case of a near-horizontal free surface, with the bulk of the fluid at the cylinder bottom, was considered in [4], where, after considerable simplification, the governing equations were reduced to ordinary differential equations. In the present study the behavior of the free surface is investigated using a creeping flow approximation. The controlling parameters vary over a wide range. In the numerical computations a boundary element method was used. The numerical results have been confirmed experimentally.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 3, pp. 25–30, May–June, 1993.     

Force Action of a Body with a Permeable Boundary on a Wall in a Fluid

The ideal fluid flow due to fluid penetration through the boundary of an infinitely long solid cylinder in contact with a solid wall is determined. A formula is derived according to which the force exerted by a finite-length part of the cylinder on the wall is directed into the wall and can thus have an arbitrarily large absolute value. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 47, No. 1, pp. 82–84, January–February, 2006.     

Measurements of layer depth during baroclinic instability in a two-layer flow

This study investigates the baroclinic instability of a two-layer rotating fluid system. The instability is generated by releasing a cylinder of buoyant fluid at the surface of ambient fluid. The buoyant fluid is dyed so that its depth may be determined from its optical thickness. The system first adjusts until the horizontal density gradient is balanced by a flow along the front, and the adjusted state is then unstable to azimuthal waves. Contours of constant upper layer depth are examined, and the perturbation at each azimuthal wavenumber is determined. The initial wavenumber is well modelled by simple quasi-geostrophic theory. There is a clear high wavenumber cutoff, and a transfer of energy to larger scales with time.     

T-RANS Simulations of Subcritical Flow with Heat Transfer Past a Circular Cylinder Surrounded by a Thin Porous Layer

We study flow and heat transfer to a cylinder in cross flow at Re = 3,900–80,000 by means of three-dimensional transient RANS (T-RANS) simulations, employing an RNG k − ε turbulence model. Both the case of a bare solid cylinder and that of a solid cylinder surrounded at some fixed distance by a thin porous layer have been studied. The latter configuration is a standard test geometry for measuring the insulating and protective performance of garments. In this geometry, the flow in the space between the solid cylinder and the porous layer is laminar but periodic, whereas the outer flow is transitional and characterized by vortex shedding in the wake of the cylinder. The results from the T-RANS simulations are validated against data from Direct Numerical Simulations and experiments. It is found that T-RANS is very well suited for simulating this type of flow. The transient nature of the flow underneath the porous layer is well reproduced, as well as the influence of vortex shedding on the heat transfer in the downstream stagnation zone. T-RANS results are found to be in much better agreement with DNS and experimental data than results from steady-state RANS.     

Perturbations on interfaces between media driven by the vertical ascent of a circular cylinder in a multilayer fluid

The initial-boundary value problem of the vertical ascent of a circular cylinder in a multilayer fluid is considered within the nonlinear theory. In each layer the fluid is ideal, incompressible, heavy, and homogeneous. At the initial instant of time the cylinder is located in the lower layer and begins smoothly to accelerate vertically from zero to a constant velocity. A system of integrodifferential equations of the problem is obtained. As unknowns, this system contains both the intensities of the singularities simulating the fluid and rigid boundaries and the functions describing the shape of the interface between the fluid media. The numerical solution of this system is based on two iteration processes, one of which is associated with time integration using the Runge-Kutta-Felberg scheme, while the other is associated with the solution of a system of linear algebraic equations obtained by discretization of the integral relations in each time step. The problem of the vertical ascent of a cylinder in a three-layer fluid (seawater, fresh water and air) is considered in detail. The results of calculating the perturbations of the fluid interfaces and the distributed and total hydrodynamic contour characteristics are given. The results obtained are compared with the solution of the problem of the ascent of a circular cylinder to the interface between water and air media. It is concluded that the third layer and the Froude number significantly affect the nature of the perturbations induced by the contour. Omsk, e-mail: gorlov@iitam.omsk.net.ru. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 2, pp. 153–159, March–April, 2000. The work was carried out with financial support from the Russian Foundation for Basic Research (project No. 96-01-00093).     

Deformation by the external flow of the surface of a magnetic fluid covering a circular cylinder

As one of the methods of controlling separation of a flow and reducing hydrodynamic resistance in flow round the body, [1] proposes covering the surface of the body with a layer of magnetic fluid maintained by a inhombgeneous field. The effectiveness of the method is studied in the example of flow rounda circular cylinder covered with a uniform layer of a magnetic fluid the surface of which is also assumed to be cylindrical and not dependent on the external flow. The resistance of the cylinder falls (if the viscosity of the magnetic fluid is not too high) and can be greatly reduced. It is of interest to determine the nature of the deformation produced in the surface of the magnetic fluid by the external flow, since the degree to which the boundary can be deformed determines whether the proposed method can be realized in practice. Moreover, the magnitude of the deformation evidently affects the resistance of the cylinder and determines the limits of the applicability of the approximation adopted in [1] for the nondeformed state of the surface.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 28–31, January–February, 1988.     

Forces acting on a coulomb crystal of microparticles in plasma

An equilibrium two-layer structure of charged microparticles in the near-electrode layer of a radio-frequency discharge was simulated numerically using the Monte Carlo method. Depending on gas pressure, the microparticles either move chaotically or form a multilayer structure with a hexagonal lattice in a horizontal plane. Based on the experiment, a mechanism is proposed that describes the unusual structure of a plasma crystal in which particles of the lower layer are located in the vertical direction strictly under the particles of the upper layer and form vertical columns. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 39, No. 6, pp. 8–15, November–December, 1998.     

Stability of the tubular layer of a deformed material in a rotating horizontal cylinder

The stability conditions for the steady-state motion of the tubular layer of a treated deformable material in a rotating horizontal cylinder are determined analytically. With allowance for the accepted similarity criteria, universal diagrams of the boundaries of transition of modes of motion of liquid and loose materials in the cylinder are obtained on the basis of experimental data. Analysis of the diagrams shows the identity of the stability conditions for a liquid layer and a loose medium, which can be regarded as a Newtonian liquid upon fast relative motions. It is shown also that the analytical stability conditions for the liquid layer correspond to the experimental data for large Reynolds numbers when the mode hysteresis occurs and do not correspond to these data for small Reynolds numbers when secondary circulating flows form. Rovno State Pedagogical Institute, Rovno 266000, Ukraine. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 41, No. 1, pp. 120–127, January–February, 2000.